Coordinates and Design
1
General Outcome
• Describe and analyze position and motion of objects and shapes.
Specific Outcomes
SS4 Identify and plot points in the four quadrants of a Cartesian plane
using integral ordered pairs.
SS5 Perform and describe transformations (translations, rotations or
reflections) of a 2-D shape in all four quadrants of a Cartesian plane
(limited to integral number vertices).
By the end of this chapter, students will be able to:
Section
1.1
Understanding Concepts, Skills, and Processes
✓ label the origin and axes of a Cartesian plane
✓ identify points on a Cartesian plane
✓ plot points on a Cartesian plane
1.2
✓ create a design on a Cartesian plane
✓ identify the points used to make a design
✓ identify the coordinates of vertices of a 2-D shape
1.3
✓ perform a translation, reflection, and rotation
✓ describe the image resulting from a transformation
1.4
✓ describe the movement of a point on a Cartesian plane using the terms
horizontal and vertical
✓ determine the horizontal and vertical distances between two points
✓ describe how the vertices of a 2-D shape change position when they are
transformed one or more times
Assessment as Learning
Supported Learning
• As students complete each section of the
Use the Before column of BLM 1–2
chapter or complete the Chapter 1 Review,
Chapter 1 Self-Assessment to provide
have them review the related parts of BLM
students with the big picture for this chapter
1–2 Chapter 1 Self-Assessment, fill in the
and to help them identify what they already
appropriate part of the During column, and
know, understand, and can do. You may wish
report what they might do about any items
to have students keep this master in their math
portfolio and refer back to it during the chapter. that they have marked either red or yellow.
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Chapter 1 Planning Chart
Section
Suggested Timing
Exercise Guide
Chapter Opener
• 20–30 minutes
Teacher’s Resource
Blackline Masters
Materials and
Technology Tools
BLM 1–1 MathLinks 7
Scavenger Hunt
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–3 Coordinates and Design
• 11 × 17 paper
• grid paper
• scissors
• ruler
• glue
• stapler
1.1 The Cartesian
Plane
• 80–100 minutes
Essential: 1a), b), 5, 7, 9, 11,
Math Link
Typical: 1a), b), one of 2, 3, or 4, 5,
7, 9, 11, 12, 14, 16, Math Link
Extension/Enrichment: 1a), b), one
of 2, 3, or 4, 13–18
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
Master 2 Two Stars and One Wish
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–4 Section 1.1 Extra Practice
BLM 1–5 Section 1.1 Math Link
• grid paper
• ruler
• 11 × 17 paper
• scissors
• glue
• computer with Internet
access (optional)
1.2 Create Designs
• 80–100 minutes
Essential: 1–3, 5, 8, Math Link
Typical: 1–3, 5, 7, 8, 10, 11,
Math Link
Extension/Enrichment: 1, 2, 8, 9,
11–14
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–6 Section 1.2 Extra Practice
BLM 1–7 Section 1.2 Math Link
• grid paper
• ruler
• coloured pencils
• computer with Internet access
(optional)
1.3 Transformations
• 120–150 minutes
Essential: 1, 2, 5, 11, 16, 19,
Math Link
Typical: 1–3, 5 11, 16, 19, 20,
Math Link
Extension/Enrichment: 1, 2, 21–25
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–8 Section 1.3 Extra Practice
BLM 1–9 Section 1.3 Math Link
• coloured pencils
• grid paper
• ruler
• scissors
• tracing paper
• Mira or mirror (optional)
• magazines
• computer with Internet
access (optional)
1.4 Horizontal and
Vertical Distances
• 80–100 minutes
Essential: 1–3, 6, 9, Math Link
Typical: 1–3, 6–9, 11, Math Link
Extension/Enrichment: 1, 2, 10–14
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–10 Section 1.4 Extra Practice
• grid paper
• ruler
• overhead projector (optional)
• computer with Internet
access (optional)
Chapter 1 Review
• 40–50 minutes
Have students do at least one question Master 8 Centimetre Grid Paper
related to any concept, skill, or process Master 9 0.5 Centimetre Grid Paper
that has been giving them trouble.
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–4 Section 1.1 Extra Practice
BLM 1–6 Section 1.2 Extra Practice
BLM 1–8 Section 1.3 Extra Practice
BLM 1–10 Section 1.4 Extra Practice
BLM 1–11 Chapter 1 Key Words Puzzle
Chapter 1
Practice Test
• 40–50 minutes
Provide students with the number of
questions they can comfortably do in
one class. Choose at least one question
for each concept, skill, or process.
Minimum: 1–3, 5–10, 13
Chapter 1
Wrap It Up!
• 80–100 minutes
• grid paper
• ruler
• scissors (optional)
• tracing paper (optional)
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–12 Chapter 1 Test
• grid paper
• ruler
• scissors (optional)
• tracing paper (optional)
Master 1 Project Rubric
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–5 Section 1.1 Math Link
BLM 1–7 Section 1.2 Math Link
BLM 1–9 Section 1.3 Math Link
BLM 1–13 Chapter 1 Wrap It Up!
• grid paper
• ruler
• coloured pencils
• scissors (optional)
• tracing paper (optional)
• string, coloured beads (optional)
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Chapter 1 Planning Chart (continued)
Section
Suggested Timing
Exercise Guide
Teacher’s Resource
Blackline Masters
Materials and
Technology Tools
Chapter 1
Math Games
• 40–50 minutes
BLM 1–14 Going Fishing
Game Boards
• coins
• coloured pencils (optional)
Chapter 1 Challenge
in Real Life
• 40–50 minutes
Master 1 Project Rubric
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–15 Chapter 1 MathLinks 7
Student Resource Answers
BLM 1–16 Chapter 1 BLM Answers
• grid paper
• scissors
• coloured pencils
• stapler
Chapter 1 Assessment Planner
Assessment Options
Type of Assessment
Assessment Tool
Chapter Opener
Assessment as Learning (TR pages i, 3)
BLM 1–2 Chapter 1 Self-Assessment
Chapter 1 Foldable
1.1 The Cartesian Plane
Assessment as Learning (TR pages 6,
8, 10)
Assessment for Learning (TR pages 10, 11,
13, 15)
Math Learning Log (TR page 10)
Master 2 Two Stars and One Wish
BLM 1–2 Chapter 1 Self-Assessment
1.2 Create Designs
Assessment as Learning (TR pages 13,
15, 17)
Assessment for Learning (TR pages 14,
16, 17)
Math Learning Log (TR page 17)
BLM 1–2 Chapter 1 Self-Assessment
1.3 Transformations
Assessment as Learning (TR pages 20,
24, 28)
Assessment for Learning (TR pages 21, 22,
26, 29)
Math Learning Log (TR page 28)
BLM 1–2 Chapter 1 Self-Assessment
1.4 Horizontal and Vertical Distances Assessment as Learning (TR pages 31,
33, 35)
Assessment for Learning (TR pages 32, 34)
Math Learning Log (TR page 35)
BLM 1–2 Chapter 1 Self-Assessment
Chapter 1 Review
Assessment for Learning (TR page 36)
Assessment as Learning (TR page 37)
Math Learning Log (TR page 37)
BLM 1–2 Chapter 1 Self-Assessment
Chapter 1 Practice Test
Assessment as Learning (TR page 38)
Assessment of Learning (TR page 39)
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–12 Chapter 1 Test
Chapter 1 Wrap It Up!
Assessment of Learning (TR page 39a)
Master 1 Project Rubric
Chapter 1 Math Games
Assessment for Learning (TR page 40)
Chapter 1 Challenge in Real Life
Assessment for Learning (TR page 40a)
Assessment of Learning (TR page 40a)
Master 1 Project Rubric
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You may wish to use one or more of the following materials to help you
assess student readiness for Chapter 1.
Assessment for Learning
Method 1: Have students develop
a journal entry to explain what
they personally know about
number lines, coordinate grids,
and transformations, and when
they might have used graphing and
transformations to make designs
of different shapes.
Supported Learning
• Students who require reinforcement of prerequisite
skills may wish to complete the Get Ready materials
available in the MathLinks 7 Workbook and at the
www.mathlinks7.ca book site.
Method 2: Have students complete
BLM 1–3 Coordinates and
Design to check their conceptual
understanding. Remind students
that you are looking for the scope
of their knowledge.
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Suggested Timing
20–30 minutes
Materials
• 11 × 17 paper
• grid paper
• ruler
• scissors
• glue
• stapler
Blackline Masters
BLM 1–1 Math Links 7
Scavenger Hunt
BLM 1–2 Chapter 1
Self-Assessment
Key Words
Cartesian plane
x-axis
y-axis
origin
quadrants
coordinates
vertex
transformation
translation
reflection
rotation
What’s the Math?
In this chapter, students learn about the coordinate grid. They start by
identifying and labelling the parts of a coordinate grid. They then learn how
to identify and plot points. Students move on to creating designs and locating
shapes by identifying the vertices. Students also learn how to perform
transformations: translations, reflections, and rotations. Finally, they
describe how the vertices of a 2-D shape change in position, horizontally
and vertically, when they are transformed.
Activity Planning Notes
Introduce students to the various parts and aspects of the MathLinks 7
student resource by having them complete BLM 1–1 MathLinks 7
Scavenger Hunt.
Then start Chapter 1 by explaining that the chapter is about using geometric
transformations to create cultural designs. This will involve plotting points
and creating shapes on a coordinate grid. Discuss with students when they
have used graphing and transformations—translations, reflections, and
rotations—to make designs with different shapes.
Before students open the student resource, have them
complete a web on a blank 11 × 17 paper to show what
they remember from previous years about the term
coordinate grid (or Cartesian plane, depending on the
term that they are most familiar with).
coordinate
grid
Encourage students to free associate any ideas they may have or remember.
Allow them to use words, diagrams, drawings, and numbers in their free
association. Collect these webs to help you to discover what students already
know and what they have misconceptions about. Allow students to hand
in a blank piece of paper, as you may choose to revisit this activity at the
end of the chapter so that students may add concepts that they have learned
through the course of the chapter.
Math Link
Aboriginal peoples from all over the world use beads and designs to
decorate their ceremonial clothing and other items. Have students
research some of these designs in the library, in magazines, on the
Internet, and through other sources of information, like an Elder. At
the end of the chapter, students will have an opportunity to create
a bead design of their own. In this chapter, students will learn how
to plot points and how to translate designs so that they can make a
plan for their design.
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Supported Learning
FOLDABLES TM
Study Tool
Learning Style
• Create a space in your classroom
Have students make the Foldable in the student resource to keep
track of the information in the chapter.
You may wish to have students keep track of Key Words using
a design specifically for that purpose. Students can make the
following Foldable and write vocabulary terms on the front of each
tab. Have them use the space beneath the tab to write definitions and
provide examples.
Step 1
Cut a sheet of grid paper horizontally in half.
Fold the half sheet in two horizontally.
Fold here
Step 2
Draw a line 2 cm from the left side of the folded paper.
Cut the top part of the fold along this line.
where students can post questions
and comments on sticky notes
under the headings “Questions I
Still Have” and “Things I’m Not Sure
About.” These notes will help you
address issues as they arise. Names
should be optional.
Meeting the Needs of
All Learners
• Invite a person who does beading
to show some patterns that include
transformations. Also, you may
wish to show students these two
publications: Copper and Caribou
Inuit Skin Clothing Production by
Jillian Oakes (Canadian Museum
of Civilization, 1991) and Sinews
of Survival: The Living Legacy of
Inuit Clothing by Betty Kobayashi
Issenman (UBC Press, 1997).
2 cm
Step 3
Make one of these folded sheets
for each Key Word. Staple the tabs
together to make a booklet.
Step 4
Write a Key Word on the front of
each tab. Write definitions and
give examples underneath the tabs.
Note: You can have students make the complete vocabulary Foldable
at the beginning of the chapter, or have them add the number of tabs
needed for each section as they do it.
Assessment as Learning
Chapter 1 Foldable
As students work on each section
in Chapter 1, have them keep track
of any problems they are having
under the What I Need to Work On
tab in their chapter Foldable.
Supported Learning
• As students complete each section, have them review
the list of items they need to work on and then have
them check off any that have been handled.
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1.1
The Cartesian Plane
Suggested Timing
80–100 minutes
Materials
• grid paper
• ruler
• 11 × 17 paper
• scissors
• glue
• computer with Internet access (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
Master 2 Two Stars and One Wish
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–4 Section 1.1 Extra Practice
BLM 1–5 Section 1.1 Math Link
Mathematical Processes
✓
✓
Communication
Connections
Mental Mathematics and Estimation
✓
✓
✓
✓
Problem Solving
Reasoning
Technology
Visualization
Specific Outcomes
SS4 Identify and plot points in the four quadrants of a Cartesian plane using integral ordered pairs.
Warm-Up
5. Draw a coordinate grid and plot the following points:
1. Draw a number line from -10 to 10 and label it by 5s.
2. For each letter on the number line, identify the integer.
S –5
Q –3 –2 –1
R
1
2
3
4
P
6
3. Draw a number line from –5 to 5. Plot the following
points on it:
A3
B -1
J(2, 3), K(5, 0), L(0, 0), and M(4, 5).
Mental Math
6. Skip count by 2s from 0 to 10.
7. Skip count by 5s from 0 to 25.
8. Skip count by 10s from 0 to 100.
C0
D -5
9. Skip count by 2s from 40 to 50.
4. For each of the following ordered pairs, identify the
x-coordinate and the y-coordinate.
b) (2, 7)
a) (5, 1)
c) (0, 9)
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Answers
Warm-Up
1.
–10
–5
0
5
10
2. P 5, Q -4, R 0, S -6
3.
D –4 –3 –2 B C
1
2 A
4
5
4. a) x = 5, y = 1 b) x = 2, y = 7 c) x = 0, y = 9
5. y
M
4
J
2
K
L
0
2
4
x
6. 0, 2, 4, 6, 8, 10 7. 0, 5, 10, 15, 20, 25
8. 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
9. 40, 42, 44, 46, 48, 50
Explore the Math
1. c) O(0, 0)
2. e) x-coordinates are positive; y-coordinates are positive.
In quadrant I, all x-coordinates and y-coordinates will
be positive.
f) In quadrant II, x-coordinates are negative and
y-coordinates are positive. In quardrant III,
x-coordinates and y-coordinates are negative.
In quadrant IV, x-coordinates are positive and
y-coordinates are negative.
Activity Planning Notes
Start the lesson by inviting students to relate a time when they were lost.
Explain that maps were created to help people find their way and that this
lesson deals with using grids to understand location.
Read the short explanation about the Cartesian plane. Tell students that
Descartes came up with the idea of the Cartesian plane when he was lying
sick in bed and saw a fly on the ceiling. He thought that he should be able
to describe the exact location of the fly to his nurse and realized a grid
would make it possible.
Explore the Math
Start students off by explaining that they will be creating a Foldable. The
coordinate grid will be glued into the Foldable. You may wish to have students
create the Foldable prior to drawing the axes on the paper, so that they have an
idea of where they need to draw their lines on the grid paper. It is a good idea
to have an example made prior to class to show to students.
As students label the quadrants, direct their attention to the Literacy Link
about Roman numerals. Then ask why Roman numerals are used to describe
the quadrants (to avoid confusion with the numbers on the axes).
3. quadrant I: (+, +); quadrant II:
(-, +);
quadrant III: (-, -); quadrant IV:
(+, -)
Supported Learning
ESL
• Some students might not
understand the word map. Have a
map to show to students. Since the
words horizontal and vertical are
key to this lesson, have students
draw these lines in their notebooks
and/or show with their bodies what
these lines look like.
Common Errors
• Some students may not remember
horizontal and vertical.
Rx Post a reminder on the wall that
shows a line labelled vertical and
a line labelled horizontal.
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Answers
Show You Know: Example 1
T(2, -3), R(-6, -4), A(-5, 0), I(-1, 6), N(0, 3)
Supported Learning
ESL, Language, and Memory
• Ensure students understand the terms ordered pair,
x-coordinate, and y-coordinate.
ESL
• Students are asked to make a “prediction” in the Explore
the Math. Assist students with their understanding of
this word, and encourage them to add it to their
translation dictionary.
Motor
• Students may find it more manageable to create their
coordinate grid using Master 8 Centimetre Grid Paper,
instead of Master 9 0.5 Centimetre Grid Paper.
Meeting the Needs of All Learners
• Work through the Explore the Math at least twice. Have
students tell you what to do as you draw the coordinate
grid the second time.
• If possible, bring in a map of your community or region.
Give students plenty of time to examine the map and locate
places they have visited. This exploration will help tie their
learning into their experiences. Use the map to support
your discussion of the coordinate grid.
Assessment as Learning
Supported Learning
Reflect on Your Findings
Listen as students discuss what
symbols should go on each door of
their Foldable. During this process,
they are generalizing what they
have learned during the Explore
the Math.
• Encourage students to develop a memory device to
help them remember that the x-coordinate comes
before the y-coordinate. For example, x comes before
y in the alphabet.
• Have students design a class poster showing the
coordinate grid with labelled parts. Hang it in the
classroom for easy reference.
After students complete the Example 1 Show You Know, have them share
their answers with a classmate.
Assessment for Learning
Example 1
Have students do the
Show You Know related
to Example 1.
Supported Learning
• Encourage kinesthetic and concrete learners to walk through
the steps. For example, they may wish to run their finger
across the x-axis to find the x-coordinate, and then run their
finger up or down the y-axis to find the y-coordinate.
• You may wish to provide additional points on a coordinate
grid for students who would benefit from extra practice:
a) Place B at (2, 0). (Some students may need practice in
moving on only one axis.)
b) Place C at (6, -6). (Some students may confuse the
coordinates when they have a pair with a negative
number and a positive number. Remind them to identify
the x-coordinate first.)
Coach students through a), and then have them try b) on
their own.
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Answers
Show You Know: Example 2
y
10
A
8
6
4
C
2
–10 –8 –6 –4 –2 0
–2
–4
–6
–8
–10
2
4
6 8 10 x
R
Common Errors
• Some students may place the labels for the x-axis and
y-axis incorrectly.
Rx Remind students to label the x-axis under the horizontal
number line and the y-axis on the left side of the vertical
number line. Refer them to the Foldable they created for
the Explore the Math.
• Some students may draw a coordinate grid with intervals
that are unequal.
Rx Give students opportunities to gain greater
understanding by studying the intervals on rulers
and other gradient materials, like measuring cups,
thermometers, etc.
Consider inviting someone from the community to speak about cultural
philosophies on the stars and the universe. For example, a Cree Elder may
talk about how the Cree philosophies are based on the coordinate grid and
on everything being in relation to the origin. To Inuit, the Big Dipper is
generally thought to represent a caribou or a group of caribou. In Inuktitut,
it is called Tukturjuk or Tukturjuit (plural). You may wish to refer to The
Arctic Sky: Inuit Astronomy, Star Lore, and Legend, John MacDonald
(Royal Ontario Museum, 1998).
Supported Learning
Learning Style
• Students may benefit from helping
to create a coordinate grid on the
floor of the class using masking
tape. As you teach the location of
points, have them walk to locate
the point.
Have students look at Example 2. Ask how the exercise is the same or
different from Example 1. Again, have students share their answers upon
completing the Show You Know.
Assessment for Learning
Example 2
Have students do the
Show You Know related
to Example 2.
Supported Learning
• You may wish to have students who would benefit from it
plot additional points on their coordinate grid:
a) Plot D at (1, -9). (Having student do the reverse pair that
they did in the original exercise.)
b) Plot O at (-8, -4). (Some students may have more
difficulty working in quadrant III).
c) Plot G at (-8, 0). (Check that students remember how to
handle a point on one of the axes.)
Coach students through a), and then have them try b) and c)
on their own.
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Answers
Communicate the Ideas
1. a) Answers may vary. For example: The first number in
the ordered pair is the x-coordinate. Find the value on
the x-axis. The second number is the y-coordinate.
Find this value on the y-axis. Find a line through the
y-coordinate and parallel to the x-axis. Find a line
through the x-coordinate and parallel to the y-axis. Where
the two lines intersect is where the point is located.
b) Answers may vary. For example: From the point, run
your finger directly up or down to the x-axis. The number
on the x-axis is the x-coordinate. From the point, run
your finger left or right to the y-axis. The number on
the y-axis is the y-coordinate. Place the two values in
brackets separated by a comma (x, y).
2. a) Answers may vary. For example: Grid A and Grid B
share the same ranges for the x-axis and y-axis. Grid A
has all the integer values listed for its range of numbers,
but Grid B does not.
b) Answers may vary.
y
3. Answers may vary. For example:
Similarity: Both points are located
on an axis.
Difference: The point (0, 3) is on
the y-axis and the point (3, 0) is
on the x-axis.
4
2
0
(0, 3)
(3, 0)
2
4 x
4. a) Answers may vary. For example: Describe the fly’s
location as up/down, left/right from a recognized point
(e.g., a light).
b) It would be possible to describe the location of the fly in
a very precise way, by identifying the x-coordinate and
y-coordinate on the grid.
Key Ideas
Have students relate the Key Ideas to the Communicate the Ideas. For
example, you might point out that the Key Idea “An ordered pair (x, y) is
used to locate any point on a coordinate grid” relates to #1.
Communicate the Ideas
The Communicate the Ideas gives students an opportunity to explain their
understanding of plotting coordinate points on a plane. In addition, students
are provided the opportunity to apply their understanding by discussing how
to describe the position of a fly in #4.
Assessment as Learning
Supported Learning
Communicate the Ideas
Have all students complete #1,
and then have students choose
one or two of the other three
questions to respond to in
their journals.
• Encourage students to consider their own learning style
when answering #1. More abstract learners may understand
what quadrant to move to depending on the signs of the
numbers in the pair.
• Use Master 2 Two Stars and One Wish to have students
critique another student’s response to #3. This master allows
them to write two things they like about a piece and one
thing they would improve. Work with the class to develop
criteria for judging the response.
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Supported Learning
ESL
• English language learners may have difficulty with
questions that involve a lot of text. In the Communicate
the Ideas, students should be encouraged to use their first
language to answer the questions and then translate their
ideas to you. (This strategy allows students to demonstrate
their understanding in detail rather than be hindered by
their understanding of the language.)
• In Communicate the Ideas #4, students are asked to
imagine a fly. Some students may not know what a fly is
and how big it would be. Provide a picture and a visual
estimate of the size.
Category
Question Numbers
Essential (minimum questions to cover
the outcomes)
1a), b), 5, 7, 9, 11, Math Link
Typical
1a), b), one of 2, 3, or 4, 5, 7, 9, 11, 12, 14, 16,
Math Link
Extension/Enrichment
1a), b), one of 2, 3, or 4, 13–18
Practise
Have students work in pairs or groups of up to four. Students should discuss
the work and agree on answers.
Assessment for Learning
Practise
Have students do #5, #7,
and #9. Students who have
no problems with these
questions can go on to the
Apply questions.
Supported Learning
• Students who have problems with #5 and #7 will need
additional coaching with Example 1. Have these students
explain how they are identifying coordinates. Clarify any
misunderstandings. Coach students through point G in #6
and point A in #8, and then have them complete the rest of
these questions on their own.
• Students who have problems with #9 will need additional
coaching with Example 2. Have these students explain how
they are plotting points. Clarify any misunderstandings.
Coach students through point J in #10, and then have them
complete the rest of this question on their own.
• Check back with them several times to make sure that they
understand the concepts.
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Supported Learning
ESL and Language
• For #14, students may need to have the concepts of traffic
lights and crosswalks explained to them, especially if they
are new to Canada or living in a small isolated community.
• A lot of reading is required for #11 to #16. Assign only
one or two questions for students as it will take them
longer to deal with the language.
ESL
• Extend #18 refers to Hurricane Katrina. This is a cultural
reference that may be unfamiliar to recent immigrants
to Canada. Explain what happened and where the
hurricane occurred.
Learning Style and Memory
• You may wish to provide BLM 1–4 Section 1.1 Extra
Practice to students who require more practice. You will
find the answers to this master on BLM 1–16 Chapter 1
BLM Answers.
Apply and Extend
For #15b), students may need to be reminded that the area of a rectangle is
found by multiplying the length by the width. Refer students to the Literacy
Link: Finding Area.
For #17b), allow students to determine the lengths either by measuring with
a ruler or by plotting the points on centimetre grid paper. You may wish to
provide students with Master 8 Centimetre Grid Paper.
Assessment as Learning
Supported Learning
Math Learning Log
Have students reflect on
two or three items they have
improved on and how they
think they have improved.
Have students also pick a
weaker area and reflect on
how they plan to improve
this area of learning.
• Have students check the What I Need to Work On section
of their chapter Foldable. Encourage them to keep track of the
items that are giving them difficulty and to check off each
item as the problem is resolved.
• Work with students to develop a plan for dealing with the areas
in which they are having difficulty.
• Depending on students’ learning style, have them provide oral
or written answers.
• Have students review the part related to section 1.1 in
BLM 1–2 Chapter 1 Self-Assessment, fill in the appropriate
part of the During column, and report what they might do about
any items that they have marked either red or yellow.
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Answers
Math Link
a) A(2, 2), B(3, 3), C(4, 4), D(5, 5), E(-2, 2), F(-3, 3),
G(-4, 4), H(-5, 5), I(-2, -2), J(-3, -3), K(-4, -4),
L(-5, -5), M(2, -2), N(3, -3), O(4, -4), P(5, -5)
b) Answers may vary. For example: Each quadrant has beads
with similar coordinate pairs (i.e., the numbers are the same
but the signs vary).
Allow students to work as a group online to
practise their skills with the coordinate grid. Go to
www.mathlinks7.ca and follow the links. Have
someone report the findings of the group to the class.
Assessment
for Learning
Math Link
The Math Link on
page 11 is intended
to help students work
toward the chapter
problem wrap-up titled
Wrap It Up! on page 39.
Supported Learning
• Encourage students to notice what happens
to a design when they use the same numbers
in each quadrant of a coordinate plane.
• Observe students as they work on the Math
Link, making sure that they identify the
correct coordinates and report on what they
notice about the coordinates of the design.
• Have students explain to a partner how they
discovered the pattern.
• Students who are having difficulty getting
started could use BLM 1–5 Section 1.1
Math Link, which provides scaffolding
for this activity.
MATH LINK
This Math Link is part of the
chapter problem introduced
in the Math Link in the chapter
opener. Doing this activity will
assist students with the Wrap It
Up! at the end of the chapter.
This activity also helps to prepare
students for section 1.2, in
which they will create designs
on a coordinate grid, and for
section 1.3, in which they
perform transformations. You
may wish to discuss briefly with
students how the design in this
Math Link might have been
created using transformations.
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1.2
Create Designs
Suggested Timing
80–100 minutes
Materials
• grid paper
• ruler
• coloured pencils
• computer with Internet access (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–6 Section 1.2 Extra Practice
BLM 1–7 Section 1.2 Math Link
Mathematical Processes
✓
✓
Communication
Connections
Mental Mathematics and Estimation
✓
✓
Problem Solving
Reasoning
Technology
✓
Visualization
Specific Outcomes
SS4 Identify and plot points in the four quadrants of a Cartesian plane using integral ordered pairs.
Warm-Up
3. Draw a coordinate grid with axes from 0 to 8. Plot
1. Draw a coordinate grid. Label the axes by 2s from
–10 to 10.
2. Identify the coordinates of points J, K, L, and M.
y
6
J
Mental Math
K
4 M
4. Skip count by 2s from 80 to 100.
5. Skip count by 5s from 35 to 50.
2
0
the following points: A(1, 2), B(3, 8), C(5, 8),
D(7, 8), E(7, 6), F(7, 4). Use a ruler to join the
points in alphabetical order. Join F to A. What
shape do you see?
6. Skip count by 10s from 90 to 150.
L
2
4
6x
7. Skip count backward by 2s from 10 to 0.
8. Skip count backward by 5s from 25 to 0.
9. Skip count backward by 10s from 50 to 0.
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Answers
Warm-Up
y
10
8
1.
6
4
2
–10 –8 –6 –4 –2 0
–2
2
4
6
x
8 10
–4
–6
–8
–10
2. J(2, 6), K(5, 5), L(1, 1), M(0, 4)
3. y
8
B
C
D
E
6
F
4
2
A
0
2
8x
6
4
Answers may vary. For example: kite or quadrilateral
4. 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
Activity Planning Notes
5. 35, 40, 45, 50
Discuss with students which types of logos and flags would
be easier to draw on a coordinate grid and why (logos and
flags with straight lines).
6. 90, 100, 110, 120, 130, 140, 150
Explore the Math
Have students check each other’s work to make sure that
the increments are equally spaced and that the points are
in the correct position on the coordinate grid.
7. 10, 8, 6, 4, 2, 0 8. 25, 20, 15, 10, 5, 0
9. 50, 40, 30, 20, 10, 0
Explore the Math
1.—3.
y
10
D
Q
N
Assessment as Learning
Supported Learning
Reflect on Your Findings
Listen as students discuss
whether connecting the
points in a different order
would result in a different
design. During this process,
they are expanding their
understanding of what they
have learned during the
Explore the Math.
• If students are unfamiliar with the Red
Cross Symbol, they might briefly research
this organization on the Internet.
• Encourage students to develop steps for
creating a design. For example:
– Plot the vertices of the design.
– Identify and label the vertices.
– Connect the vertices.
– Colour the design (if it has colour).
You may wish to record these steps on
a poster to hang in the classroom.
–10
A
5
P
0
–5
M L
K –5
–10
C
E
F
I
J
G
5
H
10 x
B
4. a) Answers may vary. For example: The Red Cross symbol
b) Answers may vary. For example: No, each point (or
set of coordinates) has nine different points that it can
connect to that will change the shape.
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Answers
Show You Know: Example 1
F(-3, 6), I(-1, 5), G(1, 6), U(1, 2), R(-1, 3), E(-3, 2)
Show You Know: Example 2
Answers will vary. Look for clear, logical instructions.
Communicate the Ideas
1. Answers may vary. For example: Place the design on a
coordinate grid as a series of vertices. Label each vertex
with an ordered pair and/or letter. State the order in which
the ordered pairs and/or letters are to be connected.
2. Answers may vary. For example: The instructions give
exact locations for each vertex and line to be drawn.
Supported Learning
ESL
• Terms that some English language
learners might have difficulty with
include logo, flag, design, brand,
symbol, and different order.
• Be sensitive to the fact that not
all students come from languages
that use the English alphabet.
Explore the Math #2 has students
connect the dots in alphabetical
order. Post an alphabet on the
wall or provide an alphabet for
students.
Language
• For students who have difficulty
with language, you may wish
to allow them to explain their
instructions for the Example 2 Show
You Know orally.
Once students complete the Example 1 Show You Know individually, have
them check each other’s work. Make sure that students agree about where
the coordinates lie.
Assessment for Learning
Example 1
Have students do the Show You
Know on page 13 related to
Example 1.
Supported Learning
• Encourage kinesthetic and concrete learners to run
their finger across the x-axis to find the x-coordinate,
and then run their finger up or down the y-axis to find
the y-coordinate.
Ask them to compare their flag in Example 2 with a classmate’s. Divide
students into pairs for the Show You Know and have them try to follow
the instructions for drawing their partner’s square.
Assessment for Learning
Example 2
Have students do the Show You
Know related to Example 2.
Common Errors
• Some students may have difficulty
counting up and down by 2s, 5s,
and 10s.
Rx Many opportunities in the
classroom to “skip count” would
help students with this problem.
Supported Learning
• You may wish to provide students with Master 9
0.5 Centimetre Grid Paper. Students with motor
difficulties may have more success using Master 8
Centimetre Grid Paper.
• Make sure students understand that the vertices of
a shape must lie on intersecting grid lines of the
coordinate grid.
• You might have students research and design a flag of
their choice.
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Supported Learning
ESL
• In Communicate the Ideas, students are asked to explain
each step when creating a design on a coordinate grid.
Teach the English language learners in the class transition
words such as first, then, after, before, next, and following.
Students could also show the steps visually.
Communicate the Ideas
The Communicate the Ideas is intended to allow students to explain their
understanding of creating a design on the coordinate plane and identifying the
coordinates of the vertices.
Assessment as Learning
Communicate the Ideas
Have all students complete
#1 individually, and then
complete #2 as a class.
Supported Learning
• For #1, some students may prefer to sketch a design on
a plain piece of paper before plotting the vertices on a
coordinate grid.
• For #2, direct students to create a simple design that is not
on a coordinate grid. Have them write instructions for the
design and exchange with a classmate.
Category
Question Numbers
Essential (minimum questions to cover
the outcomes)
1–3, 5, 8, Math Link
Typical
1–3, 5, 7, 8, 10, 11, Math Link
Extension/Enrichment
1, 2, 8, 9, 11–14
Practise
Students may need to be reminded of the names of shapes and what they
look like before doing #3 and #4. Shapes that may need to be reviewed are
square, triangle, parallelogram, rectangle, trapezoid, and arrow.
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Supported Learning
Learning Style and Memory
• You may wish to provide BLM 1–6 Section 1.2 Extra
Practice to students who require more practice.
Assessment for Learning
Supported Learning
Practise
• Students who have problems with #3 and #5 will need
Have students do #3 and #5.
additional coaching. Have these students explain how they
Students who have no problems
are identifying coordinates of vertices and describing how
with these questions can go on
to create a design. Clarify any misunderstandings. Coach
to the Apply questions.
students through Figure C in #4 and Design A in #6, and then
have them complete the rest of each question on their own.
Apply and Extend
For #8, be aware that students may want to create some inappropriate words
on the grids. Brainstorm appropriate four-letter words as a class.
For #11, have students create a similar climate graph for the community in
which they live.
For #12, students may benefit from using a table to list the lengths and
widths as ordered pairs, for example:
Length
Width
Ordered Pair
1
17
(1, 17)
2
16
(2, 16)
Students may need to be given grid paper to determine the perimeter of the
rectangles. You may wish to provide them with Master 9 0.5 Centimetre
Grid Paper. Have students refer to the Literacy Link on page 17 to remind
them of the formula for perimeter.
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Answers
Math Link
a), b)
y
5
–5
R
Y
Y
Y
R
Y
Y
Y
R
B
G
G
Y
B
G
G
Y
B
B
Y
Y
Y
B
Y
Y
Y
B
B
G
G
Y
B
G
G
Y
B
R
Y
Y
Y
R
Y
Y
Y
R
B
G
G
Y
B
G
G
Y
B
B
Y
Y
Y
B
Y
Y
Y
B
B
G
G
Y
B
G
G
Y
B
R
Y
Y
Y
Y
Y
Y
Y
R
5 x
–5
R = red
B = black
Y = yellow
G = green
or
y
5
–5
R
Y
Y
Y
R
Y
Y
Y
R
B
G
G
Y
B
Y
G
G
B
B
Y
Y
Y
B
Y
Y
Y
B
B
G
G
Y
B
Y
G
G
B
R
Y
Y
Y
R
Y
Y
Y
R
B
G
G
Y
B
Y
G
G
B
B
Y
Y
Y
B
Y
Y
Y
B
B
G
G
Y
B
Y
G
G
B
R
Y
Y
Y
R
Y
Y
Y
R
5 x
–5
Students could add #13 and #14 to their art portfolios, explaining
how the piece of art is relevant to the study of mathematics.
Assessment
as Learning
Math Learning Log
Have students reflect
on two or three items
they have improved on
and how they think they
have improved. Have
students also pick one
weaker area and have
them reflect on how
they plan to improve in
this area of learning.
Assessment
for Learning
Supported Learning
• Have students check the What I Need to
Work On section of their chapter Foldable.
Encourage them to keep track of the items
that are giving them difficulty and to check
off each item as the problem is resolved.
• Depending on students’ learning style, have
them provide oral or written answers.
• Have students review the part related to
section 1.2 in BLM 1–2 Chapter 1 SelfAssessment, fill in the appropriate part of
the During column, and report what they
might do about any items that they have
marked either red or yellow.
Supported Learning
Math Link
• Have students do this Math Link to
The Math Link on
consolidate their understanding of drawing
page 17 is intended
designs and to prepare them for section 1.3.
to help students work
• Students who are having difficulty getting
toward the chapter
started could use BLM 1–7 Section 1.2
problem wrap-up titled
Math Link, which provides scaffolding
Wrap It Up! on page 39.
for this activity.
MATH LINK
Doing this activity will assist
students with the Wrap It Up! at
the end of the chapter. You may
wish to have students explore
different ways of repeating
the design since it could be
translated or reflected (see the
two possible solutions in the
Math Link answers above).
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1.3
Transformations
Suggested Timing
120–150 minutes
Materials
• coloured pencils
• grid paper
• ruler
• scissors
• tracing paper
• Mira or mirror (optional)
• magazines
• computer with Internet access (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–8 Section 1.3 Extra Practice
BLM 1–9 Section 1.3 Math Link
Mathematical Processes
✓
✓
Communication
Connections
Mental Mathematics and Estimation
✓
✓
✓
✓
Problem Solving
Reasoning
Technology
Specific Outcomes
Visualization
SS5 Perform and describe transformations (translations,
rotations or reflections) of a 2-D shape in all four quadrants
of a Cartesian plane (limited to integral number vertices).
Warm-Up
6. What quadrant is the shape in #5 in?
1. Sketch a coordinate grid. Label each quadrant.
How do you know?
2. Draw a vertical line 3 cm long.
Mental Math
3. Plot each point on a coordinate grid: A(4, 4),
7. Skip count by 10s from 210 to 300.
B(4, -4), C(-4, -4), and D(-4, 4). Join the
points in alphabetical order. Join D to A.
8. Skip count backward by 2s from 90 to 60.
4. What shape did you make in #3?
5. Identify the coordinates of
the vertices of the shape
using ordered pairs.
9. Skip count backward by 5s from 105 to 75.
y
10. Skip count backward by 10s from 190 to 90.
0
–2
–4
2
4
6
F
8
x
–6
–8
G
H
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Answers
Warm-Up
y
4
1.
2.
Quadrant II
Quadrant I
2
–4 –2 0
–2
Quadrant III
Quadrant IV
–4
3.
4x
2
y
4
D
A
2
–4 –2 0
–2
2
4
–4
C
x
B
4. a square
5. F(5, -2), G(1, -8), H(8, -8)
6. This shape is in quadrant IV. The signs are +, -.
7. 210, 220, 230, 240, 250, 260, 270, 280, 290, 300
8. 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60
9. 105, 100, 95, 90, 85, 80, 75
10. 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 90
Activity Planning Notes
Have students study the visual on page 18 and describe
any transformations they see. Students will likely notice
the reflection of the mountains in the water. You may
wish to point out that the kayak moving across the water
is a translation. Invite students to share other real-life
examples of transformations.
Explore the Math
There are three concepts to present to students in this
Explore the Math: translation, reflection, and rotation.
The first part deals with a translation, or slide. Have
students look at the coordinates of ΔABC and see if they
can see a relation to the new coordinates of ΔA'B'C'.
Ask them to identify a pattern for what happens to the
x-coordinate and what happens to the y-coordinate after
the translation.
Explore the Math
1., 2.
A’
y
4
A
C’
B’
2
B
C
2
–2 0
–2
4
6
8
10 12 x
3. A'(8, 5), B'(6, 3), C'(10, 3)
4., 5.
y
A
B
2
C
0
2
–2 C’
–4
4
6
B’
8 x
A’
6. a) same distance b) same distance c) same distance
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Answers
Explore the Math
7.—9.
y
6
A’
4
B
C
C’
2
A
2
–2 0
4
B’
D D’
6 8
10 12 x
10. Answers may vary. For example:
a) The figures are the same shape (congruent). The figures
are in different positions on the graph.
b) The lines are equal in length.
Show You Know: Example 1
y
–4 –2 0
E
–2
S
L
D
–4
I
–6
4x
2
E’
S’
D’
L’
I’
Supported Learning
ESL
• Words that some English language
learners might have difficulty with
in the Explore the Math include
outline, flip, mark, label, compare,
counterclockwise, and clockwise.
Have students add these words to
their translation dictionary.
Meeting the Needs of
All Learners
• Ask a quilt maker to come in
and talk to students about quilt
patterns, which often include
transformations. Show some
examples, such as in the book
Morning Star Quilts: A Presentation
of the Work and Lives of Northern
Plains Indian Women by Florence
Pulford (Leone Publications, 1989).
Have students create their own
quilt pattern on a coordinate grid.
Discuss how reflections are mirror images. The “mirror” is the line of
reflection. It is important for students to understand that the part of the object
closest to the line of reflection will also be closest on the other side of the line
of reflection. Ask why we say that a figure is “flipped” when it is reflected.
The concept of rotations sometimes gives students difficulty. Make sure
students understand that a centre of rotation, like a line of reflection, can
be placed anywhere on the coordinate grid. Rotations can be clockwise or
counterclockwise, and they can be any angle (90°, 180°, 270°, and 360° are
covered in this chapter).
Assessment as Learning
Supported Learning
Reflect on Your Findings
Listen as students discuss the
characteristics of translations,
reflections, and rotations.
During this process, they are
generalizing what they have
learned during the Explore
the Math.
• Encourage students to experiment with several objects and
a Mira or mirror. Discuss what they notice as they reflect
different objects.
• Spend time making sure students understand the more
challenging concept of rotations. Reinforce the vocabulary:
centre of rotation, clockwise, counterclockwise, angle of
rotation, etc.
• Ask students how the transformations are alike and how they
are different to help reinforce their understanding.
Have students work independently through Example 1. Ask them to predict
what would have happened if the translation had been 9 units right and
4 units down, 6 units left and 5 units up, or 8 units left and 4 units down.
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Answers
Show You Know: Example 2
y
4
2
0
–2
L
I
F
F’
2
4
L’
r
P
P’
6
8
x
I’
Supported Learning
Motor
• Students with dexterity problems
Assessment for Learning
Supported Learning
Example 1
• You may wish to have students who would benefit from it
Have students do the Show You
perform additional translations on the figure in Example 1:
Know on page 20 related to
a) Translate 1 unit left and 1 unit down. (Students first
Example 1.
practise with a translation similar to the example.)
b) Translate 4 units right and 2 units up. (Monitor how
students manage a translation similar to the Show
You Know.)
c) Translate 6 units down. (Check that students know
how to handle a translation in only one direction.)
Coach students through a), and then have them try b) and c)
on their own.
As students work through Example 2, make sure that they understand that
however many units away from the line of reflection point E is, point E' is
the same distance away on the other side of the line of reflection, and that
this is also the case for points F, G, and H.
Assessment for Learning
Supported Learning
Example 2
• You may wish to have students who would benefit from it
Have students do the Show You
perform additional reflections on the figure in Example 2:
Know related to Example 2.
a) Reflect the figure in the y-axis. (Students first practise
with a reflection similar to the example.)
b) Reflect the figure in the x-axis. (Students perform a
reflection in a horizontal line of reflection as in the Show
You Know.)
Coach students through a), and then have them try b) on
their own.
may benefit from creating the
coordinate grids on Master 8
Centimetre Grid Paper instead
of Master 9 0.5 Centimetre Grid
Paper since the larger grid will
allow them to make their drawings
on a larger scale.
The Inuit syllabic alphabet
is written using shapes. A
small part of the alphabet is
shown below.
i
u
a
pi
pu
pa
mi
mu
ma
Students may enjoy working
out how to reflect and rotate
one symbol to form the other
symbols. For more information
on Inuktitut, including the
complete syllabic alphabet, go
to www.mathlinks7.ca.
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Supported Learning
Learning Style
• You may wish to have students show you different
rotations as a physical activity. Have students turn 90°,
180°, 270°, and 360° in a clockwise and counterclockwise
direction. It may help some students to relate the centre
of rotation to the pivot foot in basketball or to relate
rotation to the hand on a clock.
Meeting the Needs of All Learners
• Consider inviting someone to speak about the significance
of clockwise and counterclockwise directions in cultural
ceremonies. For example, an Elder in the community might
talk about how all the parts of a ceremony are done in a
clockwise direction.
Remind students as they work individually through Example 3 that it is
important that the pencil tip is held securely in place while the tracing is
being turned, but not so firmly that the paper might tear.
Assessment for Learning
Supported Learning
Example 3
• You may wish to have students who would benefit from it
Have students do the Show You
perform additional rotations on the figure in Example 3:
Know on page 23 related to
a) Rotate the figure 180° clockwise about the origin.
Example 3.
(Students first practise with a rotation that is visually
more straightforward.)
b) Rotate the figure 90° counterclockwise about centre of
rotation (1, -1). (Students perform a rotation that is
slightly more challenging.)
Coach students through a), and then have them try b) on
their own.
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Answers
Show You Know: Example 3
y
T
6
U
4
N
R
–4
N’
T’
R’ 2
A
U’
–2 0
x
2
Supported Learning
Meeting the Needs of All Learners
• Provide students with additional examples of translations,
reflections, and rotations, which they should continue to
solve concretely using cutouts of the shapes. Once students
are able to perform the transformations using cutouts, move
on to plotting the coordinates to transform each shape.
y
4
Depending on your students’ grasp of rotations, you may
wish to introduce another method: the “robotic arm.”
Demonstrate how to use this method by rotating ΔABC
90° clockwise about a centre of rotation at (-1, -1). Have
students draw an arm that traces how many units left or
right then up or down the centre of rotation is from the
closest vertex. Students then rotate the arm 90° clockwise
and redraw the arm in its new position.
2
–6
–4
–2
B
A
0
2 x
–2
–4
C
At the end of the arm, they draw the point for the closest
vertex and then they plot the rest of the vertices.
y
4
Concrete and kinesthetic learners may benefit from
following this method using a tracing of the triangle and
robotic arm and then rotating the tracing by holding a
pencil at the centre of rotation.
B’
2
C’
A’
–6
–4
B
–2
A
C
0
2 x
–2
–4
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Answers
Communicate the Ideas
1. Answers may vary. For example:
a) driving in Calgary, which is laid out in a grid fashion
b) a face reflected in a mirror
c) a lazy Susan cupboard
2. Answers may vary. For example:
Translation: Move the square 2 units right, and then
3 units up.
Reflection: Reflect the square in a line of reflection along
the x-axis.
Rotation: Rotate the square 90° clockwise about a centre
of rotation at (-1, -1).
Communicate the Ideas
The Communicate the Ideas gives students an opportunity to explain their
understanding of transformations and apply it to a real-world scenario. The
transformation of the square allows students to explain their thinking in
achieving the different types of transformations.
Assessment as Learning
Communicate the Ideas
Have all students complete #1
and #2.
Supported Learning
• For #1, students with language difficulties might draw
a picture to illustrate the transformations, or they might
find pictures of transformations in magazines. They can
then identify the transformations and explain in their
own way how the pictures represent the transformations.
• As students work on #2, observe them for correct use
of the terms related to each type of transformation.
Reinforce the vocabulary as necessary.
• Have students share with a partner the transformations
that they made to the square in #2. Sharing will allow
them to verbalize their thinking and check each
other’s understanding.
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Common Errors
• Some students may have difficulty with the language of
this section.
Rx Tying the vocabulary to words they already know will
help students remember the new words. Finding real-life
examples of the transformations will also help students
remember and make sense of the concepts.
Category
Question Numbers
Essential (minimum questions to cover
the outcomes)
1, 2, 5, 11, 16, 19, Math Link
Typical
1–3, 5, 11, 16, 19, 20, Math Link
Extension/Enrichment
1, 2, 21–25
Practise
There are many opportunities for students to work on the different
transformations in the Practise section. Have students choose from a list of
questions or options (see the table above). Research shows that students do
better when they have a choice in how they work. Allow students to work
in groups. Plan to spend time observing them as they work. Exemplars of
what the work should look like (preferably more than one) will help the
struggling learners.
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Many of M.C. Escher’s works of art will provide students
with examples of transformations. It is also a lot of
fun to try to create some Escher art. This might be
an opportunity to collaborate with the art teacher.
Have students research the life and work of this
artist. To visit the official web site for M.C. Escher,
go to www.mathlinks7.ca and follow the links.
Assessment for Learning
Supported Learning
Practise
Have students do #5, #11, and #16.
Students who have no problems
with these questions can go on to
the Apply questions.
• Students who have problems with #5 will need
additional coaching with Example 1. Have these
students explain how they are performing translations.
Clarify any misunderstandings. Coach students through
#3a), and then have them complete #3b) on their own.
Then encourage them to complete #6 independently.
• Students who have problems with #11 will need
additional coaching with Example 2. Have these
students explain how they are performing reflections.
Clarify any misunderstandings. Coach students through
#9, and then have them complete #10 on their own.
Then encourage them to complete #12 independently.
• Students who have problems with #16 will need
additional coaching with Example 3. Have these
students explain how they are performing rotations.
Clarify any misunderstandings. Coach students through
#13, and then have them complete #14 on their own.
Then encourage them to complete #17 independently.
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Supported Learning
Learning Style
• As students work on the Practise, Apply, and Extend
questions, help to focus their learning by asking
them questions.
Apply and Extend
The Apply questions give students opportunities to justify their thinking.
Make sure that students fully explain their answers, especially for #19 to
#21 and #23.
For #25, students who have fully grasped the concept of transformations
should understand how some translations can make an image that appears
the same. For students who still might be having difficulty with this notion,
ask them to translate and reflect a square. Have them explain how the
squares are alike and how they are different after the transformations.
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Supported Learning
Learning Style and Memory
• You may wish to provide BLM 1–8 Section 1.3 Extra
Practice to students who require more practice. For
enrichment with this blackline master, tell students that
there are other letters on which you can draw a vertical or
a horizontal line of reflection so that the letter reflects on
itself. Ask them which letters they are, and have them draw
the letters and the lines of reflection.
Students are expected to learn many concepts in this lesson. It is important
that time be given to develop the ideas presented in section 1.3 before
moving on to section 1.4.
Assessment as Learning
Supported Learning
Math Learning Log
Have students reflect on
two or three items they have
improved on and how they
think they have improved.
Have students also pick one
area in which they feel they
did not learn as much as they
should or could have. Have
them reflect on how they
plan to improve in this area
of learning.
• Have students check the What I Need to Work On section of
their chapter Foldable. Encourage them to keep track of the
items that are giving them difficulty and to check off each
item as the problem is resolved.
• Work with students to develop a plan for dealing with the
areas in which they are having difficulty.
• Depending on students’ learning style, have them provide oral
or written answers.
• Have students write about strategies that have helped them
understand transformations.
• Invite students to write an acrostic poem about
transformations using the stem TRANSFORMATIONS.
• Keep a record of student reflections in their learning portfolio.
You may wish to have them return to these reflections at the
end of the chapter.
• Have students review the part related to section 1.3 in
BLM 1–2 Chapter 1 Self-Assessment, fill in the appropriate
part of the During column, and report what they might do about
any items that they have marked either red or yellow.
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Answers
Math Link
Answers may vary. For example:
a) translation 3 units right
b)
y
5
R
R
R
B
R
R
R
–5
R = red
B = blue
B
R
R
B
R
R
B
B
B
B
B
B
B
B
R
R
R
B
R
R
R
B
R
R
B
R
R
B
B
B
B
B
B
B
B
x
–5
c) I reflected the design in the x-axis.
MATH LINK
Doing this activity will assist students with the Wrap It Up!
at the end of the chapter. As they work on the Math Link,
observe how students decide which transformation to
apply, and look for logic and order in their description of
the transformation.
Assessment for Learning
Math Link
The Math Link on page 29 is
intended to help students work
toward the chapter problem
wrap-up titled Wrap It Up!
on page 39.
Supported Learning
• You may wish to have students do this Math Link in
order to provide them with practice in identifying and
performing transformations.
• Observe students as they work on the Math Link, making
sure that they identify the transformations and perform their
own transformation correctly.
• Have students explain their transformation to a partner.
• Students who are having difficulty getting started could
use BLM 1–9 Section 1.3 Math Link, which provides
scaffolding for this activity.
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1.4
Horizontal and
Vertical Distances
Suggested Timing
80–100 minutes
Materials
• grid paper
• ruler
• overhead projector (optional)
• computer with Internet access (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–10 Section 1.4 Extra Practice
Mathematical Processes
✓
✓
Communication
Connections
Mental Mathematics and Estimation
✓
✓
✓
✓
Problem Solving
Reasoning
Technology
Visualization
Specific Outcomes
S5 Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four
quadrants of a Cartesian plane (limited to integral number vertices).
Warm-Up
2. Sketch a coordinate grid with each axis labelled by
1. Identify the coordinates of the vertices of
figure QRST.
2s from -5 to 5.
3. On the grid from #2, plot the following points:
R(4, 5), I(5, 0), G(1, -5), H(-3, -1), T(-2, 2).
y
4. Draw a horizontal line 5 cm long.
0
–2
R
–2
2
4
x
Q
5. Draw an example of a reflection.
Mental Math
6. Skip count backward by 10s from 500 to 410.
–4
S –6
7. Skip count backward by 5s from 185 to 100.
T
8. Skip count backward by 2s from 1000 to 980.
9. Skip count backward by 10s from 290 to 210.
10. Skip count by 5s from 1005 to 1045.
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Answers
Warm Up
1. Q(3, –2), R(–1, –2), S(–1, –6), T(3, –6)
2., 3.
y
R
4
T
2
I
–4
–2 0
H
–2
2
4
x
–4
G
4.
5. Answers will vary. For example:
G’
H’
y
F’ 4
2
E’
–4 –2 0
r
E
2
F
4
G
H
6 x
6. 500, 490, 480, 470, 460, 450, 440, 430, 420, 410
7. 185, 180, 175, 170, 165, 160, 155, 150, 145, 140, 135,
130, 125, 120, 115, 110, 105, 100
8. 1000, 998, 996, 994, 992, 990, 988, 986, 984, 982, 980
9. 290, 280, 270, 260, 250, 240, 230, 220, 210
10. 1005, 1010, 1015, 1020, 1025, 1030, 1035, 1040, 1045
Activity Planning Notes
Explore the Math
As a class, brainstorm examples of video games and
board games involving movement on a grid.
Explore the Math
Provide students with Master 9 0.5 Centimetre Grid
Paper or Master 8 Centimetre Grid Paper for drawing
their coordinate grids. Have students share their solutions
to #3 with the class by demonstrating their transformations
on an overhead projector, if available.
Assessment as Learning
Reflect on Your Findings
Listen as students discuss what
transformations would move the
ball into the glove. During this
process, they are generalizing
what they have learned during
the Explore the Math.
Supported Learning
• As a class, compose a statement
about transformations between
two fixed points. For example:
“Different transformations may
be used to get from one fixed
point to another, but the total
distance does not change.”
1. a) (4, 2)
b) 1 unit horizontally right, 1 unit vertically up
c) 2
2. 9 units horizontally right, 5 units vertically up
3. Answers may vary. For example:
a) Rotate the ball 180° clockwise about the point (1, 1),
and then translate the ball 1 unit horizontally left and
1 unit vertically down
b) Reflect the ball in the y-axis, and then translate the ball
1 unit horizontally right and 5 units vertically up.
c) Translate the ball 9 units horizontally right and 5 units
vertically up.
Show You Know: Example 1
Answers will vary. Check for accuracy and that students use
each type of transformation.
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Supported Learning
ESL
• Words that some English language learners might have
difficulty with in the Explore the Math include travel,
position, and total. Have students add these words to their
translation dictionary.
• Note that some students may come from a country where
people do not play baseball and golf. It is important that
students understand the objective of these sports in order
to make a connection to the lesson.
Motor
• You may wish to provide Master 8 Centimetre Grid Paper
to students with dexterity problems to that they can draw
their coordinate grids on a larger scale.
Meeting the Needs of All Learners
• Introduce these activities using paper cutouts or game
markers that can be physically moved over the grid. Then
introduce the counting of units and plotting on the grid.
• Use the coordinate grid on the floor to have students
physically perform the transformations outlined in the
Explore the Math.
Have students work through Example 1 independently, and then direct them
to come up with two solutions for the Show You Know.
Give students the opportunity
to play the golf game online by
going to www.mathlinks7.ca
and following the links.
Assessment for Learning
Supported Learning
Example 1
• Have students work in groups to share and test each other’s
Have students do the Show You
solutions to Example 1.
Know on page 31 related to
• You may wish to encourage students who would benefit from
Example 1.
it to come up with more straightforward transformations that
will put the golf ball into the hole:
a) Use one translation.
b) Use one reflection and one translation.
Coach students through a), and then have them try b) on
their own.
After completing Example 2, discuss whether the distance would change if
the order of the transformations changed.
Assessment for Learning
Supported Learning
Example 2
• Encourage kinesthetic and concrete learners to use their
Have students do the Show You
fingers to count the number of units left or right and then up
Know on page 33 related to
or down to determine the movement of the vertex.
Example 2.
• You may wish to have students who would benefit from
it also describe the movement of vertices M, O, and E.
(Students will note that the distance each vertex moved
is different from the others.)
Coach students through vertex M, and then have them try
vertices O and E on their own.
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Answers
Show You Know: Example 2
a)
y
V’
8
M
E
V“
6
4 O
A
O’
2
V
–4
–2 0
–2
E’
M’ O“
2
4
E“
6 M“8
10 x
b) (10, 6)
c) Vertex V moved 15 units horizontally right and 6 units
vertically up to vertex V.
Communicate the Ideas
1. a) A to A': 1 unit horizontally left, 6 units vertically up;
A' to A'': 8 units horizontally right
b) B to B': 1 unit horizontally left, 6 units vertically up;
B' to B'': 4 units horizontally right
c) It is different because image A''B''C''D'' is a reflection
of ABCD and not a translation.
2. Answers may vary. For example: Point E has been
translated 3 units horizontally right rather than 3 units
vertically up.
Key Ideas
In their journals, have students state how the two Key Ideas are alike and
how they are different.
Communicate the Ideas
The Communicate the Ideas is intended to allow students to explain their
understanding of the change in position of a point by counting horizontal
and vertical movements. It also allows students to answer why the positional
changes are different for the different vertices of a shape.
Assessment as Learning
Supported Learning
Communicate the Ideas
• In #1c), students have the opportunity to express in their
Have students complete #1 and own words the learning from Example 2.
#2 in pairs, and then discuss
• For students who have had difficulty with the terms
#1c) and #2 as a class.
horizontal and vertical, #2 gives them a chance to clarify
their thinking.
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Category
Question Numbers
Essential (minimum questions to cover
the outcomes)
1–3, 6, 9, Math Link
Typical
1–3, 6–9, 11, Math Link
Extension/Enrichment
1, 2, 10–14
Practise
Have students work in groups to complete the Practise questions. Make sure
that they describe the movement using the words vertical and horizontal.
Encourage students to check each other’s work as they complete it.
Assessment for Learning
Supported Learning
Practise
• Students who have problems with #3 will need additional
Have students do #3 and #6.
coaching with Example 1. Have these students explain how
Students who have no problems
they are identifying horizontal and vertical movement of
with these questions can go on
a point. Clarify any misunderstandings. Coach students
to the Apply questions.
through point A in #4, and then have them complete the rest
of the question on their own.
• Students who have problems with #6 will need additional
coaching with Example 2. Have these students explain how
they are identifying horizontal and vertical movement of
vertices. Clarify any misunderstandings. Coach students
through point K in #5, and then have them complete the rest
of the question on their own.
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Supported Learning
ESL
• Words that some English language learners might have
difficulty with in the Apply section are bridge, closest,
and comic strip. Have students add these words to their
translation dictionary.
Learning Style and Memory
• You may wish to provide BLM 1–10 Section 1.4 Extra
Practice to students who require more practice.
Apply and Extend
For #10, tell students that their cartoon character may end up right side up,
sideways, or upside down in the different quadrants. Explain that they should
create a comic strip that incorporates these positions in a fun way. Once they
are completed, display the comic strips. Students might add them to their
portfolios, along with an explanation of how the comic strip was created.
Consider using #11 as a journal question. It could also be used for a
creative writing piece by some of the more literary students.
Assessment as Learning
Supported Learning
Math Learning Log
Have students reflect on
two or three items they have
improved on and how they
think they have improved.
Have students also pick one
area in which they feel they
did not learn as much as they
should or could have. Have
them reflect on how they
plan to improve in this area
of learning.
• Have students check the What I Need to Work On section of
their chapter Foldable. Encourage them to keep track of the
items that are giving them difficulty and to check off each
item as the problem is resolved.
• Work with students to develop a plan for dealing with the
areas in which they are having difficulty.
• Depending on students’ learning style, have them provide oral
or written answers.
• Keep a record of student reflections in their learning portfolio.
You may wish to have them return to these reflections at the
end of the chapter.
• Have students review the part related to section 1.4 in BLM 1–2
Chapter 1 Self-Assessment, fill in the appropriate part of the
During column, and report what they might do about any items
that they have marked either red or yellow.
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1
Chapter Review
Suggested Timing
40–50 minutes
Materials
• grid paper
• ruler
• scissors (optional)
• tracing paper (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–4 Section 1.1 Extra Practice
BLM 1–6 Section 1.2 Extra Practice
BLM 1–8 Section 1.3 Extra Practice
BLM 1–10 Section 1.4 Extra Practice
BLM 1–11 Chapter 1 Key Words Puzzle
Assessment
for Learning
Supported Learning
Chapter 1 Review
• Have students revisit the
The Chapter 1 Review
concept web that they created
is an opportunity for
in the Chapter Opener so that
students to assess
they may add concepts that
themselves by
they have learned through
completing selected
the course of the chapter.
questions in each section
Students might make these
and checking their
additions in a different
answers against the
colour so that you can see
answers in the back of
what they have learned.
the student resource.
• Have students check the
contents of the What I Need
to Work On tab of their
chapter Foldable and do at
least one question related to
each item on that tab.
• Have students revisit any
section that they are having
difficulty with prior to
working on the chapter test.
Activity Planning Notes
For #1 to #9 of the Chapter 1 Review, students may wish
to review the words in pairs. One student could read the
definition and the other could say the word. They may
want to do the exercise backward: one student could read
the word and the other could find the definition. As an
alternative to or in addition to this exercise, give students
BLM 1–11 Chapter 1 Key Words Puzzle.
Have students work individually to place the numbers 10
to 21 in two columns in their notebooks. Instruct them to
look at the question related to the number in the Chapter 1
Review and decide how well they understand it. Tell them
to circle each number according to the colours they used
on BLM 1–2 Chapter 1 Self-Assessment.
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Supported Learning
Learning Style
• Allow students to continue to use tracing paper and
cutouts, as necessary, to perform rotations.
Learning Style and Memory
• Students who require more practice on a particular topic
may refer to the following blackline masters: BLM 1–4
Section 1.1 Extra Practice, BLM 1–6 Section 1.2 Extra
Practice, BLM 1–8 Section 1.3 Extra Practice, and
BLM 1–10 Section 1.4 Extra Practice.
Gifted and Enrichment
• Some students may already be familiar with skills
handled in this review. To provide questions for
enrichment and extra challenge for gifted students,
go to www.mathlinks7.ca and follow the links.
Assessment as Learning
Supported Learning
Math Learning Log
• Have students use the What
Once students have completed the Chapter 1 Review,
I Need to Work On section of
have them reflect on the chapter as a whole. Ask them
their chapter Foldable to provide
to answer at least three of the following questions.
information about what they
– What two or three things did you find easy? Why?
continue to have problems with
– What surprised you in the chapter? Why?
and what problems they had that
– What was fun in the chapter? Why?
have now been resolved.
– What concepts did you find difficult? What help do you
• You may wish to have students
need to understand these concepts? How will you get the
refer to BLM 1–2 Chapter 1
help you need?
Self-Assessment when they
– How well do you understand the chapter? Explain.
report on what they found easy
– How would you explain the main concepts of the chapter
and how well they understand
to someone in a letter?
the chapter.
– When might you or someone else use the concepts in
this chapter in real life?
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Practice Test
1
Suggested Timing
40–50 minutes
Materials
• grid paper
• ruler
• scissors (optional)
• tracing paper (optional)
Blackline Masters
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–2 Chapter 1 Self-Assessment
BLM 1–12 Chapter 1 Test
Assessment
as Learning
Chapter 1
Self-Assessment
Have students
review their earlier
responses on
BLM 1–2 Chapter 1
Self-Assessment.
Supported Learning
• Have students use their
responses on the practice test
and work they completed
earlier in the chapter to
complete the After column
of this self-assessment. Before
the chapter test, coach them
in the areas in which they are
having problems.
Study Guide
Question(s)
Section(s)
Refer to
I can …
1, 2, 5
1.1
Explore
the Math
Example 2
✓ identify points on a Cartesian plane
3
1.3
Example 2
✓ perform a reflection
4
1.3
Example 3
✓ perform a rotation
6, 8
1.2
Example 1
✓ identify the coordinates of the vertices of a 2-D shape
7
1.3
Example 1
Example 3
✓ perform a translation
✓ perform a rotation
9, 10
1.3
Explore
the Math
✓ perform a translation, a reflection, and a rotation
✓ describe the image resulting from a transformation
11
1.4
Example 2
✓ describe how the vertices of a 2-D shape change position when they are transformed
one or more times
12, 14
1.3
Examples 1,
2, 3
✓ perform a translation, a reflection, and a rotation
13
1.4
Explore
the Math
Example 1
✓ describe the movement of a point on a Cartesian plane using the terms horizontal
and vertical
✓ determine the horizontal and vertical distance between two points
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Supported Learning
Learning Style
• Allow kinesthetic and concrete learners to use tracing
paper and cutouts to perform rotations as they work on
the test.
• You may wish to differentiate for some students the
questions you feel they must know, the questions they
should know, and the questions that are nice to know.
Activity Planning Notes
Have students start the practice test the same way they
started the chapter review—by writing the question
numbers in their notebooks and circling each number
according to the colours they used for BLM 1–2
Chapter 1 Self-Assessment. Have students first complete
the questions they know they can do. Then have them
complete the questions they know something about. Finally,
have them do their best on the questions that they are still
struggling with.
Assessment
of Learning
Supported Learning
Chapter 1 Test
• Consider allowing students to
After students
use their chapter Foldable.
complete the practice • Consider using the Math Games
test, you may wish
on page 40 or the Challenge in
to use BLM 1–12
Real Life on page 41 to assess
Chapter 2 Test as a
the knowledge and skills of
summative assessment. students who have difficulty
with tests.
This practice test can be assigned as an in-class or takehome assignment. These are the minimum questions
that will meet the related curriculum outcomes: #1–#3,
#5–#10, and #13.
Answers to the Chapter 1 Practice Test are provided
on BLM 1-15 Chapter 1 MathLinks 7 Student
Resource Answers.
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Wrap It Up!
Suggested Timing
80–100 minutes
Materials
• grid paper
• ruler
• coloured pencils
• scissors (optional)
• tracing paper (optional)
• string, coloured beads (optional)
Blackline Masters
Specific Outcomes
Master 1 Project Rubric
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
BLM 1–5 Section 1.1 Math Link
BLM 1–7 Section 1.2 Math Link
BLM 1–9 Section 1.3 Math Link
BLM 1–13 Chapter 1 Wrap It Up!
Common Errors
• Some students may not have
included a transformation in
their design.
Rx Have them look at some class
exemplars to help them come
up with ideas.
• Some students may not have
reflected their designs properly.
Rx You may wish to have students
copy the designs onto tracing
paper to help them with the
reflections.
SS4 Identify and plot points in the four quadrants of a
Cartesian plane using integral ordered pairs.
SS5 Perform and describe transformations (translations,
rotations or reflections) of a 2-D shape in all four quadrants
of a Cartesian plane (limited to integral number vertices).
Activity Planning Notes
As a class, brainstorm some helpful hints so that all students can feel
successful in developing the design. For example:
• Get an idea of how much space you have by counting a rectangle of
30 beads. (Include the two axes in your counting.)
• As you draw the transformations, make note of the transformations you use.
• First, draw all the beads that will lie on the axes, and then fill in the rest of
the beads of your design.
Assessment of Learning
Wrap It Up!
This chapter problem wrap-up
gives students an opportunity to
use and display their knowledge
of transformations on a coordinate
grid in a useful and artistic way.
It is important for students to use
mathematical language in their
descriptions of their designs.
Master 1 Project Rubric provides
a holistic descriptor that will assist
you in assessing student work on
this Wrap It Up! Page 39a provides
notes on how to use this rubric for
the Wrap It Up!
Supported Learning
• You may wish students to review the work they have
completed in the Math Links in sections 1.1, 1.2, and
1.3 before they begin.
• If students have not completed the Math Links, you
may wish to provide them with BLM 1–5 Section 1.1
Math Link, BLM 1–7 Section 1.2 Math Link, and
BLM 1–9 Section 1.3 Math Link.
• If students have difficulty creating a design,
– reduce the number of beads they must use
– do not expect them to include transformations
– have them copy a simple design
• Observe how accurately students transform their
designs and describe their transformations.
• If you have time, allow students to re-create their
designs using real beads.
• Consider inviting someone from the community
who does beading to show patterns that include
transformations. This person might help students
re-create their designs with real beads.
• You may wish to have students use BLM 1–13
Chapter 1 Wrap It Up!, which provides scaffolding
for the chapter problem wrap-up.
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The chart below shows the Master 1 Project Rubric for tasks such as the
Wrap It Up! and provides notes that specify how to identify the level of
specific answers for the project.
Score/Level
5
(Standard of
Excellence)
4
(Above
Acceptable)
3
(Meets
Acceptable)
2
(Below
Acceptable)
1
(Beginning)
Holistic Descriptor
❑ Applies/develops thorough strategies and
mathematical processes making significant
comparisons/connections that demonstrate a
comprehensive understanding of how to develop
a complete solution
❑ Procedures are efficient and effective and may
contain a minor mathematical error that does
not affect understanding
❑ Uses significant mathematical language to explain
their understanding and provides in-depth support
for their conclusion
Specific Question Notes
• provides a complete solution with one or
more initial transformations
• includes reflections that may contain a
minor point error that does not affect
the understanding
• provides an explanation that is clear
and complete
• provides a complete design with at least
❑ Applies/develops thorough strategies and
one initial transformation
mathematical processes for making reasonable
• plots points with some errors present
comparisons/connections that demonstrate a clear
as a result of the transformation and/or
understanding
reflection (two at most)
❑ Procedures are reasonable and may contain a
• includes a clear explanation that addresses
minor mathematical error that may hinder the
most of the requirements
understanding in one part of a complete solution
❑ Uses appropriate mathematical language to explain
their understanding and provides clear support for
their conclusion
❑ Applies/develops relevant strategies and
mathematical processes making some comparisons/
connections that demonstrate a basic understanding
❑ Procedures are basic and may contain a major
error or omission
❑ Uses common language to explain their
understanding and provides minimal support
for their conclusion
• creates a basic design with only one initial
transformation
• makes some errors in the transformations
• includes a minimal explanation
❑ Applies/develops some relevant mathematical
processes making minimal comparisons/
connections that lead to a partial solution
❑ Procedures are basic and may contain several
major mathematical errors
❑ Communication is weak
• creates a design that is missing several of
the basic requirements for the initial design
• fails to include the transformation, or the
transformation has an error and/or the
reflection is in one axis only
• provides little or no explanation
❑ Applies/develops an initial start that may be
partially correct or could have led to a correct
solution
❑ Communication is weak or absent
• begins design in one quadrant
or
• draws a design that does not contain a
transformation attempt, and a reflection may
be attempted but many errors are present
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Math Games
Suggested Timing
40–50 minutes
Materials
• coins
• coloured pencils (optional)
Blackline Masters
BLM 1–14 Going Fishing Game Boards
Supported Learning
ESL
• Words that some English language learners might have
difficulty with include locations, touch, overlap, hit, and
miss. Take the time to explain the game using visuals
to show students what it means if they hit or miss a
coordinate. Hit and miss in this context have different
meanings from what students may be more familiar with.
Meeting the Needs of All Learners
• Have students use alternatives that are most familiar to
them, for example, animals of different lengths such as fox,
seal, polar bear, caribou; or cars of different lengths.
Common Errors
• Some students may repeat guesses that they have
already made.
Rx Make sure students mark all their guesses, both correct
and incorrect, on the bottom game board of the BLM.
Specific Outcomes
SS4 Identify and plot points in the four quadrants of a Cartesian plane using integral ordered pairs.
Activity Planning Notes
Read through the game with students. You might want to mention that the
given values are the approximate lengths of full-grown fish in metres. Discuss
with students games similar to this one that they may have played before.
Assessment for Learning
Going Fishing
Have students play this
game with a partner of
similar math ability.
Supported Learning
• You may wish to give each student a copy of BLM 1–14
Going Fishing Game Boards.
• Encourage students to record their guesses using correct
notation for ordered pairs.
• After students have played the game one or more times,
brainstorm winning strategies, such as guessing points
around a hit until you catch the entire fish and keeping
track of which fish have been caught and which still need
to be located.
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Challenge in Real Life
Suggested Timing
40–50 minutes
Materials
• grid paper
• scissors
• coloured pencils
• stapler
Blackline Masters
Master 1 Project Rubric
Master 8 Centimetre Grid Paper
Master 9 0.5 Centimetre Grid Paper
Mathematical Processes
✓
✓
Communication
Connections
Mental Mathematics and Estimation
✓
✓
✓
✓
Problem Solving
Reasoning
Technology
Visualization
Specific Outcomes
SS5 Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four
quadrants of a Cartesian plane (limited to integral number vertices).
Activity Planning Notes
You may wish to use the following steps to introduce and complete
this challenge:
1. Read through Make an Animation as a class. Some students may already
make animations by drawing pictures on, and then flipping, the corners
of their notebooks. Have these students share their knowledge of how
to get items to “move” by drawing consecutive views with the object in
a slightly different position. For example, they might show a basketball
going through a basket or a gymnast doing a flip on a trampoline.
2. With the class, discuss how this idea might work on a coordinate grid.
For example, students might draw a car moving from one quadrant to
another, or they might show something more complicated, such as an
athlete moving from one field event to another. Students who do not
draw well could animate shapes or emoticons.
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Supported Learning
Learning Style
• Kinesthetic learners and concrete
learners could be encouraged to
cut out the shape that they are
going to animate and physically
move it across a coordinate grid
before they start drawing.
Motor
• For easy flipping, the stapled
booklets need to have a very
smooth edge.
Meeting the Needs of
All Learners
• Students could be encouraged to
use items and events relevant to
their cultural group.
Gifted and Enrichment
• Point out that the more sheets of
paper students use with smaller
changes in movement, the more
fluid the animation.
3. Have students work individually to make a rough sketch of the item
that they are going to animate, and consider how they will move it. You
may wish to provide Master 8 Centimetre Grid Paper or Master 9 0.5
Centimetre Grid Paper, depending on how large or small the animation
is going to be. (Students should cut the paper into pieces in order to make
the animation.)
4. Clarify that the task is to
• draw one or more animations that show a translation, reflection,
and rotation
• describe what transformations were used and how each was used
NOTE: You may wish to control the number of sheets of paper per
animation. A total of eight to ten sheets is a good starting point. At this
age, students’ ability to flip the pages is sometimes related to their small
motor skills.
5. Review the Master 1 Project Rubric with students so that they will
know what is expected.
This challenge can be used for either Assessment for Learning or
Assessment of Learning
Assessment for Learning
Supported Learning
Make an Animation
Discuss the challenge with the
class. Have students brainstorm
the types of activities they could
use for an animation, sketch
the beginning and final picture,
and then discuss what might
go in between. Students should
individually do the animation
sketches. Note that these can be
simple. It is the transformations
that are important, not the artwork.
• Review with students how to transform an object across
a coordinate grid.
• Allow students with motor difficulties to create their
animation on the corners of a notebook rather than
produce their own flip book.
• For a second challenge, complete with teaching notes
and student exemplars, go to www.mathlinks7.ca,
access the Teachers’ Site, go to Assessment, and then
follow the links.
Assessment of Learning
Supported Learning
Make an Animation
• Master 1 Project Rubric provides a holistic descriptor
Discuss the challenge with the class. that will assist you in assessing student work on this
Once students have formulated their
challenge. Page 41a provides notes on how to use this
idea and drawn a rough sketch,
rubric for this challenge.
have them share their concept with
• To view student exemplars, go to www.mathlinks7.ca,
a partner for peer feedback. Then
access the Teachers’ Site, go to Assessment, and then
have them work individually to
follow the links.
complete parts a) and b).
40a MHR • Mathematics 7: Teacher’s Resource
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The chart below shows the Master 1 Project Rubric for tasks such as
the Challenge in Real Life and provides notes that specify how to identify
the level of specific answers for this project.
Score/Level
5
(Standard of
Excellence)
4
(Above
Acceptable)
3
(Meets
Acceptable)
2
(Below
Acceptable)
1
(Beginning)
Holistic Descriptor
❑ Applies/develops thorough strategies and
mathematical processes making significant
comparisons/connections that demonstrate a
comprehensive understanding of how to develop
a complete solution
❑ Procedures are efficient and effective and may
contain a minor mathematical error that does
not affect understanding
❑ Uses significant mathematical language to explain
their understanding and provides in-depth support
for their conclusion
Specific Question Notes
• provides a complete and correct solution
with justification
• completes one or more transformations
❑ Applies/develops thorough strategies and
over the coordinate grid, describing what
mathematical processes for making reasonable
and how each was used
comparisons/connections that demonstrate a clear
• uses communication that is weak or unclear
understanding
or
❑ Procedures are reasonable and may contain a
• provides a complete solution with minor
minor mathematical error that may hinder the
errors in the vertices
understanding in one part of a complete solution
❑ Uses appropriate mathematical language to explain
their understanding and provides clear support for
their conclusion
❑ Applies/develops relevant strategies and
mathematical processes making some comparisons/
connections that demonstrate a basic understanding
❑ Procedures are basic and may contain a major
error or omission
❑ Uses common language to explain their
understanding and provides minimal support
for their conclusion
• completes one or more transformations
over the coordinate grid, describing what
transformation was used
• includes vertices that may have errors
or
• uses more than one transformation with an
error in points or application of one of the
transformations
❑ Applies/develops some relevant mathematical
processes making minimal comparisons/
connections that lead to a partial solution
❑ Procedures are basic and may contain several
major mathematical errors
❑ Communication is weak
• completes a transformation on the
coordinate grid
❑ Applies/develops an initial start that may be
partially correct or could have led to a correct
solution
❑ Communication is weak or absent
• attempts a transformation with some
coordinate points correct
• includes a response that is weak and does
not show a basic understanding
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